CHETTINAD COLLEGE OF ENGINEERING & TECHNOLOGY NH-67, TRICHY MAIN ROAD, PULIYUR, C.F , KARUR DT.

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1 CHETTINAD COLLEGE OF ENGINEERING & TECHNOLOGY NH-67, TRICHY MAIN ROAD, PULIYUR, C.F , KARUR DT. DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING COURSE MATERIAL Subject Name: Digital Communication Class / SEM: B. E. (ECE) / VI Unit - 3 PASS BAND DATA TRANSMISSION SYLLABUS Pass band Transmission Model- ML criterion-correlation receivers- Matched filters. Generation- Detection- Signal Space diagram- Bit error probability and power spectra of BPSK- QPSK- FSK and MSK schemes- Performance comparisons- carrier and bit synchronization Objective: To study about the pass band transmission model To learn about matched filters To briefly describe BPSK, QPSK, FSK and MSK schemes Comparisons of BPSK, QPSK, FSK and MSK schemes To know how to describe Signal Space diagram and Bit error probability Overview: The physically transmitted signal may be one of the following: 1. A baseband signal ("digital-over-digital" transmission): A sequence of electrical pulses or light pulses produced by means of a line coding scheme such as Manchester coding. This is typically used in serial cables, wired local area networks such as Ethernet, and in optical fiber communication. It results in a pulse amplitude modulated signal, also known as a pulse train. 2. A passband signal ("digital-over-analog" transmission): A modulated sine wave signal representing a digital bit-stream. The signal is produced by means of a digital modulation method such as PSK, QAM or FSK. The modulation and demodulation is carried out by modem equipment. This is used in wireless communication, and over telephone network local-loop and cable-tv networks.

2 Applications and history Data has been sent via non-electronic (e.g. optical, acoustic, mechanical) means since the advent of communication. Analog signal data has been sent electronically since the advent of the telephone. However, the first data electromagnetic transmission applications in modern time were telegraphy (1809) and teletypewriters (1906), which are both digital signals. Data transmission is utilized in computers in computer buses and for communication with peripheral equipment via parallel ports and serial ports such us RS-232 (1969), Firewire (1995) and USB (1996). The principle of data transmission is also utilized in storage media for Error detection and correction since Data transmission is utilized in computer networking equipment such as modems (1940), local area networks (LAN) adapters (1964), repeaters, hubs, microwave links, wireless network access points (1997), etc. In telephone networks, digital communication is utilized for transferring many phone calls over the same copper cable or fiber cable by means of Pulse code modulation (PCM), i.e. sampling and digitization, in combination with Time division multiplexing (TDM) (1962). Telephone exchanges have become digital and software controlled, facilitating many value added services. For example the first AXE telephone exchange was presented in Since late 1980th, digital communication to the end user has been possible using Integrated Services Digital Network (ISDN) services. Since the end of 1990th, broadband access techniques such as ADSL, Cable modems, fiber-to-thebuilding (FTTB) and fiber-to-the-home (FTTH) have become wide spread to small offices and homes. The current tendency is to replace traditional telecommunication services by packet mode communication such as IP telephony and IPTV. Transmitting analog signals digitally allows for greater signal processing capability. The ability to process a communications signal means that errors caused by random processes can be detected and corrected. Digital signals can also be sampled instead of continuously monitored. The multiplexing of multiple digital signals is much simpler to the multiplexing of analog signals. Because of all these advantages, and because recent advances in wideband communication channels and solid-state electronics have allowed scientists to fully realize these advantages, digital communications has grown quickly.

3 Digital communications is quickly edging out analog communication because of the vast demand to transmit computer data and the ability of digital communications to do so. The digital revolution has also resulted in many digital telecommunication applications where the principles of data transmission are applied. Examples are second-generation (1991) and later cellular telephony, video conferencing, digital TV (1998), digital radio (1999), telemetry, etc PASSBAND DATA TRANSMISSION MODEL Objective: To learn about the passband data transmission models To study about the Maximum likelihood criterion and their properties To learn about the functionality of the coorelation receivers Overview of an matched filters ML (Maximum Likelihood ) Criterion: If p 1 =p 2 = =p M, i.e. the signals {m k } are equiprobable, finding the signal that maximizes P(m k r) is equivalent to finding the signal that maximizes f(r m k ). The conditional pdf f(r m k ) is usually called the likelihood function. The decision criterion based on the maximum of f(r m k ) is called the Maximum-Likelihood (ML) criterion.

4 Maximum likelihood (ML) detection: We start with the following assumptions: Number of information-bearing signals (symbols), designed after the G-S-O approach, is M and one of these M signals is received from the AWGN channel in each time slot of T -sec. Let the messages be denoted by m i, i = 1, 2,, M. Each message, as discussed in an earlier lesson, may be represented by a group of bits, e.g. by a group of m bits each such that 2 m = M. All symbols are equi- probable. If the input message probabilities are different and known, they can be incorporated following Bayesian approach. However, for a bandwidth efficient transmission scheme, as is often needed in wireless systems, the source coding operation should be emphasized to ensure that all the symbols are independent and equally likely. Alternatively, the number of symbols, M, may also be decided appropriately to approach this desirable condition. AWGN process with a mean = 0 and double-sided psd No/2. Let w(t) denote a noise sample function over 0 t < T. Let R(t) denote the received random process with sample function over a symbol duration denoted as r (t), 0 t T. Now, a received sample function can be expressed in terms of the corresponding transmitted information-bearing symbol, say si(t), and a sample function w(t) of the Gaussian noise process simply as: r (t) = s i (t) + w(t), 0 t < T At the receiver, we do not know which s i (t) has been transmitted over the interval 0 t < T. So, the job of an efficient receiver is to make best estimate of transmitted signal [si(t)] upon receiving r(t) and to repeat the same process during all successive symbol intervals.

5 Depending on the modulation and transmission strategy, the receiver usually has the knowledge about the signal constellation that is in use. This also means that the receiver knows all the nominal basis functions used by the transmitter. For convenience, we will mostly consider a transmission strategy involving two basis functions, φ1 and φ2 (described now as unit vectors) for explanation though most of the discussion will hold for any number of basis functions. Fig. 1 shows a two-dimensional signal space showing a signal vector si and a received vector r. Fig.1 Signal space showing a signal vector si and a received vector r The job of the receiver can now be formally restated as: Given received signal vectors r, find estimates m i for all valid transmit symbols mi-s once in each symbol duration in a way that would minimize the probability of erroneous decision of a symbol on an average (continuous transmission of symbols is implicit).

6 The principle of Maximum Likelihood (ML) detection provides a general solution to this problem and leads naturally to the structure of an optimum receiver. When the receiver takes a decision that m = m i, the associated probability of symbol decision error may be expressed as: Pe (m i r) = probability of decision on receiving r that mi was transmitted = Pr (m i not sent r) = 1 Pr (m i sent r ). In the above, Pr (mi not sent r) denotes the probability that mi was not transmitted while r is received. So, an optimum decision rule may heuristically be framed as: Set m = m i if Pr (m i sent r ) Pr (m k sent r ), for all k i This decision rule is known as maximum aposteriori probability rule. This rule requires the receiver to determine the probability of transmission of a message from the received vector. Now, for practical convenience, we invoke Bayes rule to obtain an equivalent statement of optimum decision rule in terms of a priori probability: Pr (m i r ) : A posteriori probability of m i given r Pr (r ) : Joint pdf of r, defined over the entire set of signals { si(t) }; independent of any specific message m i Pr( r m i ): Probability that a specific r will be received if the message mi is transmitted known as the a priori probability of r given m i Pr(m i ) : 1/M The determination of maximum a posteriori probability is equivalent to determination of maximum a priori probability Pr( r m i ):. This a priori probability is also known as the likelihood function. So the decision rule can equivalently be stated as: Set m = m i if Pr( r m i ): is maximum for k = i

7 Usually, ln [Pr( r m i )], i.e. natural logarithm of the likelihood function is considered. As the likelihood function is non-negative, another equivalent form for the decision rule is: Set m = m i if ln [Pr( r m i )] is maximum for k = i A Maximum Likelihood Detector realizes the above decision rule.towards this, the signal space is divides in M decision regions, Zi, i = 1, 2,, M such that, Fig.2 indicates two decision zones in a two-dimensional signal space. The received vector r lies inside region Z i if ln [Pr( r m i )] is maximum for k = i. Fig. 2 Two decision zones in a two-dimensional signal space. Now for an AWGN channel, the following statement is equivalent to ML decision: Received vector r lies inside decision region Z i if, is minimum for k = i That is, the decision rule simply is to choose the signal point s i if the received vector r is closest to s i in terms of Euclidean distance.

8 So, it appears that Euclidean distances of a received vector r from all the signal points are to be determined for optimum decision-making. This can, however, be simplified. Note that, on expansion we get, It is interesting that, the first term on the R.H.S, i.e., is independent of k and hence need not be computed for our purpose. The second term is the inner product of two vectors. The third term i.e. is the energy of the k-th symbol. The received vector r lies in decision region Z i if, is maximum for k = i. That is, a convenient form of the ML decision rule is: Choose is maximum for k = i A Correlation Receiver, consisting of a Correlation Detector and a Vector Receiver implements the M L decision rule by, (a) first finding r with a correlation detector and then (b) computing the metric and taking decision in a vector receiver. Fig. 3 shows the structure of a Correlation Detector for determining the received vector r from the received signal r(t). Fig.4 highlights the operation of a Vector Receiver.

9 Fig. 3 The structure of a Correlation Detector for determining the received vector from the received signal r(t) Fig.4 Block schematic diagram for the Vector Receiver Features of the received vector r: The statistical features of the received vector r as obtained at the output of the correlation detector [Fig.3]. The j-th element of r, which is obtained at the output of the j-th correlator once in T second, can be expressed as:

10 Here w j is a Gaussian distributed random variable with zero mean and s ij is a scalar signal component of s i. Now, the mean of the correlator out put is, E[r j ] = E[s ij + w ij ] = E[s ij ] = s ij = m ij say. Note that the mean of the correlator output is independent of the noise process. However, the variances of the correlator outputs are dependent on the strength of accompanying noise: Taking the expectation operation inside, we can write Here, R w (t-u) is the auto correlation of the noise process. Additive white Gaussian noise process is a WSS random process and hence the autocorrelation function may be expressed as, R w (t, u) = R w (t- u) and further,, where No is the single-sided noise power spectral density in Watt/Hz. So, the variance of the correlator output now reduces to: The variance of the random signals at the out puts of all N correlators are

11 a) same, b) independent of information-bearing signal waveform and c) dependent only on the noise psd. Now, the likelihood function for s i (t) and the ML decision rule, can be expressed in terms of the output of the correlation detector. The likelihood function for m i = [Pr( r m i )] f r (r mi) = f r (r s i (t)) is the conditional pdf of r given m i. In our case, Self Check 1 : 1. A Correlation Receiver, consisting of a and. 2. If m = m i if Pr (m i sent r ) Pr (m k sent r ), for all k i, then this condition is known as. a) ML rule (b) Vector receiver rule (c) maximum aposteriori probability rule 3. The decision criterion based on the maximum of f(r m k ) is called. a) ML rule (b) Vector receiver rule (c) maximum aposteriori probability rule 4. The determination of maximum a posteriori probability is equivalent to determination of maximum apriori probability is known as. a) likely hood function b) power spectral density(psd) c) Joint probability 5. Say True / False: The variances of the random signals at the out puts of all N correlators are different. Problems 1) Consider a binary transmission scheme where a bit 1 is represented by +1.0 and a bit 0 is represented by 1.0. Determine the basis function if no carrier modulation scheme is used. If the additive noise is a zero mean Gaussian process, determine the mean values of r1 and r2 at the output of the correlation detector. Further, determine E1 and E2 as per Fig 4.

12 Self Check 1 Answer: 1. Correlation Detector and a Vector Receiver 2. (c) 3. (a) 4. (a) 5. False Matched Filter Objectives: Principle of matched filter (MF); Properties of a matched filter; SNR maximization and minimization of average symbol error probability; Schwartz s Inequality; What is Matched Filter? The matched filter (MF) is the optimal linear filter for maximizing the output SNR. In telecommunications, a matched filter (originally known as a North filter) is obtained by correlating a known signal, or template, with an unknown signal to detect the presence of the template in the unknown signal. This is equivalent to convolving the unknown signal with a conjugated time-reversed version of the template (cross-correlation). The matched filter is the optimal linear filter for maximizing the signal to noise ratio (SNR) in the presence of additive stochastic noise. Matched filters are commonly used in radar, in which a known signal is sent out, and the reflected signal is examined for common elements of the out-going signal. Pulse compression is an example of matched filtering. Two-dimensional matched filters are commonly used in image processing, e.g., to improve SNR for X-ray pictures. Example of matched filter in digital communications: The matched filter is used in communications. In communication system that sends binary messages from the transmitter to the receiver across a noisy channel, a matched filter can be used to detect the transmitted pulses in the noisy received signal.

13 Matched Filter Certain structural modification and simplifications of the correlation receiver are possible by observing that, (a) All orthonormal basis functions s j are defined between 0 b and they are zero outside this range. (b) Analog multiplication, which is not always very simple and accurate to implement, of the received signal r(t) with time limited basis functions may be replaced by some filtering operation. Let, h j (t) represent the impulse response of a linear filter to which r(t) is applied. Then, the filter output y j (t) may be expressed as: Now, let h j (t) = j (T-t), a time reversed and time-shifted version of j (t) Now, If we sample this output at t = T, Let us recall j (t), that is zero outside the interval 0 t T Using this, the above equation may be expressed as, From correlation receiver, we recognize that, The filter is said to be matched to the orthonormal basis function j (t), and the alternation receiver structure is known as a matched filter receiver. The detector part of the matched filter receiver is shown in [Fig.5].

14 Fig.5: The block diagram of a matched filter bank that is equivalent to a Correlation Detector A physically realizable matched filter is to be causal and h j (t) = 0 for t<0. Note that if j (t) is zero outside 0 usal impulse response. Properties of a Matched Filter A filter which is matched to a known signal (t), 0 is characterized by an impulse response h(t) which is a time reversed and delayed version of (t), i.e. h(t) = (T- t) In the frequency domain, the matched filter is characterized (without mach explanation at this point), by a transfer function, which is, except for a delay factor, the complex conjugate of the F.T. of (t), i.e. Property (1) : The spectrum of the output signal of a matched filter with the matched signal as input is, except for a time delay factor, proportional to the energy spectral density of the input signal. Let, o (f) denote the F.T. of the filter of output o (t). Then,

15 Property (2): The output signal of a matched filter is proportional to a shifted version of the autocorrelation function of the in the input signal to which the filter is matched. This property follows from Property (1). As the auto-correlation function and the energy spectral density form F.T. pair, by taking IFT we may write, Property (3): The output SNR of a matched filter depends only on the ratio of the signal energy to the psd of the white noise at the filter input. Let us consider a filter matched to the input signal (t) From property (2), we see that the maximum value of o (t) at t = T is o (T-t) = E. Now, it may be shown that the average noise power at the output of the matched filter is given by, The maximum signal power = o (T) 2 = E 2 Hence, Note that SNR in the above expression is a dimensionless quantity. This means a freedom to the designer to select specific pulse shape to optimize other design requirement (the most usual requirement being the spectrum or, equivalently, the transmission bandwidth) while ensuring same SNR.

16 Property (4): The matched-filtering operation may be separated into two matching condition: namely, spectral phase matching that produces the desired output peak at t = T and spectral amplitude matching that gives the peak value its optimum SNR. The filter is said to be matched to the signal in spectral phase if the transfer function of the filter follows: Here H(f) is real non-negative and T is a positive constant. The output of such a filter is, H(t) is real and non-negative. Spectral phase matching ensures that all spectral components of o (t) add constructively at t = T and thus cause maximum value of the output: For spectral amplitude matching, we choose the amplitude response H(f) of the filter to shape the output for best SNR at t = T by using H(f) = (f).

17 The standard matched filter achieves both these features. Maximization of output Signal to-noise Raito: Let, h(t) be the impulse response of a linear filter and x(t) = h(t) + (t), 0 h(t) is a known signal and (t) is an additive white noise sample function with zero mean and psd of (N0/2) Watt/Hz. Let, x (t) be one of the orthonormal basis functions. As the filter is linear, its output can be expressed as, y(t) = x(t) + n(t), where y(t) is the output due to the signal component x(t) and n(t) is the output due to the noise component (t).[fig.6]. Fig.5: A matched filter is fed with a noisy basis function to which it is matched We can now re-frame the requirement of minimum probability of error (or maximum likelihood detection) as: The filter should make power of 0 (t) considerably greater (in fact, as large as possible) compared to the power of n(t) at t = T.

18 That is, the filter should maximize the output signal-to-noise power ratio [(SNR)0] The following discussion shows that the SNR is indeed maximized when h(t) is matched to the known input signal x(t). Let o (f): F.T. of known signal x(t). H(f) Transfer function of the linear filter. The filter output is sampled at t = T. Now, Let, S N (f) : Power spectral density of noise at the output of the linear filter. So, Now, the average noise power at the output of the filter

19 Schwarz s Inequality or Cauchy-Schwarz inequality The Cauchy-Schwarz inequality is used to show the matched filtering maximizes the signal-tonoise ratio. Let x(t) and y(t) denote any pair of complex-valued signals with finite energy, i.e. Schwarz s Inequality states that, The equality holds if and only if This implies, a real quantity. where k is a scalar constant. Now, applying Schwarz s inequality Now, from Schwarz s inequality, the SNR is maximum i.e. the equality holds, when

20 Now, (t) is a real valued signal and hence, This relation is the same as we obtained previously for a matched filter receiver. So, we can infer that, SNR maximization is an operation, which is equivalent to minimization of average symbol error (Pe) for an AWGN Channel. Example 1: Let us consider a sinusoid, defined below as the basis function:

21 Self Study 2: 1. The optimal linear filter for maximizing the output SNR is. a) correlation receiver b) matched filter c) optimal receiver 2. is an example of matched filtering. a) image compression b) code compression c) pulse compression 3. Matched filter is otherwise called as. 4. Two dimensional matched filters are used in. a) image processing b) code compression c) pulse compression 5. Say True / False: The output SNR of a matched filter depends only on the ratio of the signal energy to the psd of the white noise at the filter input. 6. is used to show the matched filtering maximizes the signal-to-noise ratio. Problems 1. Under what conditions matched filter may be considered equivalent to an optimum correlation receiver? 2. Is a matched filter equivalent to an optimum correlation receiver if sampling is not possible at the right instants of time? 3. Explain the significance of the fact that a matched filter ensures maximum output signal-to-noise ratio. Self Study 2 Answers: 1. matched filter 2. pulse compression 3. North Filter 4. image processing 5. True 6. Cauchy-Schwarz inequality

22 Digital Modulation Techniques Objectives: To study different types of digital modulation techniques like ASK, FSK and PSK, QAM and QPSK. To learn to construct FSK transmitter and Receiver. To study about the MSK techniques. Overview: History & Development: The trend in communication is not from analog to digital but actually digital communication came first by practical means of electrical communication by using Morse code. It is a digital form of Code consisting of three elements dot, dash and space. Many of the signals in modern communication are digital. For example, codes for alphanumeric characters and binary data used in computer programs. Also digital techniques can be used for analog signal transmission. Advantages of Digitizing a Signal: Improved transmission quality. Reduction in distortion. Improvement in SNR. Types of Signal Transmission: Analog signal is sent over a channel with no modulation. For eg., the ordinary public address system consists of only microphone, amplifier, speaker and a twisted pair wire as channel. Analog Source Baseband channel Analog Destination Analog transmission is done using modulation and demodulation. It is used in radio and TV broadcasting.

23 Channel Analog Modulator Demodulator Analog Source Destination Transmitter Receiver Digital signal is transmitted through digital channel as digital pulses. Channel Digital Coder Decoder Digital Source Destination The channel can not transmit pulses directly. For example, the radio channel requires a modulation process and an ordinary telephone connection can not pass dc. The digital signal has to be modulated on to a carrier at one end and demodulated at receiver. The modem is a combination of modulator and demodulator. Analog Digital Source Modem Channel Modem Digital Destination Analog signal can be converted to digital form, transmitted and digital is converted back to analog form in receiver. Digital Analog ADC & Decoding & Analog Source Coding DAC Destination Channel The channel can not carry pulses so modulation and demodulation is required. It is used in voice transmission.

24 Analog Analog ADC & Modem Modem Decoding Analog Source Coding Channel & DAC Destination The fastest growing area in communication is the use of digital techniques with analog signal. There is no way to remove noise and distortion from analog signals since it is added cumulative in transmitter, channel and receiver. Signal to noise ratio (SNR) decreases with increase in the distance when passed through amplifiers and channels as in long distance telephone communication system. Digital signals are not immune to noise, but decrease the effect of noise and distortion. Digital system decreases the probability of error to a very small value since it uses some techniques of error detection and correction. Distortion can be removed using regenerative repeaters. Distorted Receiver Transmitter Regenerated Signal Signal Advantages of Digital Communication: Convenience in multiplexing. Mostly it is used in Time Division Multiplexing for transmitting both voice and data over same communication channel. It is most suitable for digital transmission. Convenience in switching. Disadvantages of Digital Communication: Greater Complexity. Larger transmission bandwidth. To overcome disadvantages, Large scale low cost digital ICs decreases the difficulty and expense of constructing complex circuitry. Data compression techniques with wider bandwidth media (fiber optic cable) decreases bandwidth penalty. So the advantages overweigh the disadvantages.

25 INTRODUCTION: Electronic Communication refers to transmission, reception and processing of information using electronic circuits. Information is the knowledge or intelligence communicated between two or more data points. Digital Modulation is the transmission of digitally modulated analog signal (carrier) between two or more points in a communication system. It is also called as digital radio system since digitally modulated signals can be propagated through earth s atmosphere which is used in wireless communication system. Traditional analog systems like AM, FM and PM are replaced by modern digital modulation systems. Advantages of Digital Modulation System: Ease of processing. Ease of multiplexing. High noise immunity. Digital Communication includes systems where relatively high frequency analog carriers are modulated by relatively low frequency digital information signals. It is used in digital radio systems. Digital Transmission Systems transport information in digital form and it requires a physical facility between transmitter and receiver. The physical medium can be a metallic wire pair, coaxial cable, optical fiber cable. Digital radio system uses a physical cable or free space as a communication channel. Analog and digital modulation communication system differs in the nature of the modulating signal. Both analog and digital modulation system uses analog carriers to transport information through the channel. In analog modulation, both the information and carrier are analog. In digital modulation, the

26 information is digital (computer generated data or digitally encoded analog signal) and the carrier is analog. The digital modulation system is mathematically represented as (1) If the information is digital and the amplitude (V) of the carrier is varied proportional to the digital information signal, a digitally modulated signal called Amplitude Shift Keying (ASK) is produced. If the information is digital and the frequency (f) of the carrier is varied proportional to the digital information signal, a digitally modulated signal called Frequency Shift Keying (FSK) is produced. If the information is digital and the phase (θ) of the carrier is varied proportional to the digital information signal, a digitally modulated signal called Phase Shift Keying (PSK) is produced. Quadrature Amplitude Modulation (QAM) results if both the amplitude and the phase are varied proportional to the digital information signal. ASK, FSK, PSK and QAM are all forms of digital modulation. Advantages of digital modulation: It is suited to a multitude of communication applications including both cable and wireless communication. Noise immunity is high. Several error detection and correction methods are available. Applications of digital modulation: It is used in relatively low speed voice band data communication modems in most personal computers. It is used in relatively high speed data transmission systems such as broadband digital subscriber lines (DSL). It is also used in digital microwave and satellite communication systems. It is widely used in cellular telephone personal communication systems (PCS).

27 Digital Modulation System: Figure.1 shows the simplified block diagram of digital modulation system or digital radio system. Precoder performs the level conversion. It encodes the incoming data into a group of bits that modulated an analog carrier. The modulated carrier is shaped (filtered), amplified and then transmitted through the transmission medium to the receiver. The transmission medium may be a metallic wire, optical fiber cable, earth s atmosphere or a combination of two or more types of transmission systems. In receiver, the incoming signals are filtered, amplified and then applied to the demodulator and decoder circuits which extract the original source information from the modulated carrier. The clock and carrier recovery circuits recover the analog carrier and digital timing clock signals from the incoming modulated wave since they are necessary to perform demodulation process. Shannon Limit for Information Capacity: Information theory is highly theoretical study of efficient use of bandwidth to propagate information through electronic communication systems. It is used to determine the information capacity of a data communication system.

28 Information Capacity is a measure of how much information can be propagated through a communication system. It is a function of bandwidth and transmission time. It represents the number of independent symbols that can be carried through a system in a given unit of time. The most basic digital symbol used to represent information is binary digit or Bit. It is convenient to express the information capacity of a system as a Bit Rate. Bit Rate is the number of bits transmitted during one second and is expressed in bits per second (bps). The useful relationship among bandwidth, transmission time and information capacity was given by R. Hartley of Bell Telephone Laboratories in Hartley s Law is given by, The information capacity is a linear function of bandwidth and transmission time and is directly proportional to both. Either the bandwidth or the transmission time changes, a directly proportional change occurs in information capacity also. Shannon in 1948 related the information capacity of a communication channel to bandwidth and signal to noise ratio (SNR). SNR is the ratio of signal power to noise power and is unitless. SNR in db is calculated as 10 log 10 (SNR) db. Increase in SNR provides better performance and higher the information capacity since SNR is directly proportional to the signal power. Shannon Limit for Information Capacity is

29 Problem.1: For a standard telephone circuit with SNR of 30 db and a bandwidth of 2.7 KHz, determine the Shannon limit for information capacity. Given, 10 Log 10 SNR = 30 db SNR = 10 3 = 1000 B = 2.7 KHz Then, I = 3.32 B Log 10 (1+SNR) = 3.32 x 2.7 x 10 3 Log 10 (1+1000) = 26.9 Kbps. Conclusion: 26.9 kbps information can be transmitted through a 2.7 KHz communication channel. This is true but cannot be done with a binary system. To achieve information rate of 26.9 kbps through a 2.7 KHz channel, each symbol transmitted must contain more than one bit. M-ary Encoding: M-ary is derived from the word binary. Here M represents a digit that corresponds to the number of conditions, levels or combinations possible for a given number of binary variables. It is advantageous to use a level higher than binary which is called as beyond binary or higher than binary encoding. For example, digital signal with 4 possible conditions like voltage levels, frequency, phase and time is represented as a system with M=4. The number of bits necessary to produce a given number of conditions is expressed mathematically as If N = 1, M = 2 N = 2; If N= 2, M=4; If N=3, M=8 and so on. (4)

30 Bit Rate is the rate of change of a digital information signal usually binary. Baud is the rate of change of a signal on the transmission medium after encoding and modulation have occurred. Its unit is symbols/second. Baud is a unit of transmission rate or modulation rate or symbol rate. It is also defined as the reciprocal of one output signaling element which represents several number of bits. (5) Signaling element is a symbol encoded as a change in amplitude, phase or frequency. Baud contains more than one information bit. Baud = Bit Rate in BFSK and BPSK systems. Baud < Bit Rate in QPSK and 8 PSK systems. Nyquist states that The binary digital signal can be propagated through an ideal noiseless transmission medium at a rate equal to two times the bandwidth of the medium. The minimum theoretical bandwidth necessary to propagate a signal is called Minimum Nyquist Bandwidth or Minimum Nyquist Frequency. (6) Actual bandwidth depends on the type of encoding, modulation used, type of filters used, system noise and desired error performance. Ideal bandwidth is used for comparison purposes only. For a given bandwidth B, highest theoretical bit rate is 2B. For example, a standard telephone circuit has B = 2700 Hz has a capacity of 5400 bps to propagate through it. If there is more than one level for signaling, then more than one bit is transmitted at a time and so it is possible to propagate a bit rate that exceeds 2B.

31 The Nyquist formulation for information capacity using multilevel signaling is given by The minimum bandwidth necessary to pass M-ary digitally modulated carriers is (7) (8) The information bits are encoded (grouped) and converted to signal with more than two levels. Then the transmission rate in excess of 2B is possible. Therefore, the BAUD is the encoded rate of change and is also equals to the bit rate divided by the number of bits encoded into one signaling element. (9) Baud and ideal minimum Nyquist bandwidth have the same value and is equal to the bit rate divided by the number of bits necessary to encode. This is true for all forms of digital modulation. Digital Modulation Techniques: The digital modulation techniques are classified into two types; Coherent Techniques and Noncoherent Techniques. In Coherent Technique, the receiver is equipped with a phase recovery circuit. In Noncoherent technique, there is no phase recovery circuit in the receiver. Phase recovery circuit ensures the oscillator supplying the locally generated carrier wave in the receiver is synchronized in both phase and frequency to the oscillator supplying the carrier wave used to originally modulate the incoming data stream in the transmitter.

32 In pass band data transmission, signals are generated by changing the amplitude, phase or frequency of a sinusoidal carrier in M discrete steps. The different methods of modulation are combined into a hybrid form to generate M-ary signal. For example, discrete changes in both amplitude and phase of a carrier combined to produce M- ary Amplitude Phase Shift Keying (APK). M-ary ASK is a special case of M-ary QAM. M-ary signaling is mostly used since it conserves bandwidth at the expense of increased power. Self Study 3: 1. is a unit of transmission rate or modulation rate or symbol rate. a) bit b) Hz c) baud d) db 2. The minimum theoretical bandwidth necessary to propagate a signal is called. a) Minimum Nyquist Bandwidth b) Shannon information capacity c) Baud rate 3. If both the amplitude and the phase of the information signal are varied then it is called. 4. is the number of bits transmitted during one second. a) baud rate b) symbol rate c) bit rate 5. Say True / False a) Baud > Bit Rate in BFSK and BPSK systems. c) Baud = Bit Rate in QPSK and 8 PSK systems. 6. Hartley s Law is. Self Study 3 Answers: 1. c) 2. a) 3. QAM 4. bit rate 5. a) False b) False 6.

33 Digital Amplitude Modulation (DAM) This is the simplest digital modulation technique also called as Amplitude Shift Keying (ASK). Here a binary information signal directly modulates the amplitude of an analog carrier. This is similar to standard AM except that only two output amplitudes are possible. This is also called as Digital Amplitude Modulation for this reason. Mathematically this is expressed as, (10) The modulating signal v m (t) is a normalized binary waveform where +1 V for logic 1 and -1 V for logic 0. For a logic 1 input, v m (t) = +1 V, For a logic 0 input, v m (t) = -1 V, (11) (12)

34 The modulated wave v ask (t) is either A Cos (ω C t) or 0. Therefore, the carrier is either ON or OFF. So the ASK is also referred as ON-OFF Keying (OOK). Figure.2 shows the input and output waveforms of ASK modulator. For every change in the input binary data stream, there is one change in the ASK waveform and the time of one bit (t b ) equals the time of one analog signaling element (t S ). For the entire time the binary input is high, the output is a constant amplitude constant frequency sinusoidal wave. For the entire time the binary input is low, the carrier is OFF. (13) (14) The rate of ASK waveform (baud) is same as the rate of change of binary input in bps. Therefore, bit rate = baud. With ASK, bit rate = minimum nyquist bandwidth. Therefore For ASK, N=1. (15)

35 Advantages of ASK: It is a low cost type of digital modulation technique. It is seldom used except for very low speed telemetry circuits. Disadvantages of ASK: It is a low quality system. It is susceptible to noise. Amplitude non-linearities are produced in microwave radio and satellite communication channels. It is not suitable for pass band data transmission over non-linear channels. Applications of ASK: The telephone and cable system used ASK previously but not used nowadays due to its nonlinearities and susceptibility to noise. Frequency Shift Keying (FSK): FSK is a relatively simple low performance type of digital modulation. It is a form of constant amplitude angle modulation similar to standard FM except the modulating signal is a binary signal that varies between two discrete voltage levels rather than a continuously changing analog waveform. It is also called as Binary FSK (BFSK). The general expression for BFSK signal is, The phase shift in carrier frequency ( f) is directly proportional to the amplitude of the binary input signal v m (t). The direction of the shift is determined by the polarity. The modulating signal is a normalized binary waveform where a logic 1 = +1 V and a logic 0 = -1 V.

36 For a logic 1 input, v m (t) = +1, For a logic 0 input, v m (t) = -1, With binary FSK, the center carrier frequency (f C ) is shifted (deviated) up and down in frequency domain by the binary input signal. As the binary input signal changes from a logic 0 to logic 1 and vice versa, the output frequency shifts between two frequencies (a mark or logic 1 frequency (f m ) and a space or logic 0 frequency (f S )). The mark and space frequencies are separated from the carrier frequency by peak frequency deviation ( f) and from each other by 2 f. The frequency deviation is the difference between either mark or space frequency and center frequency or half the difference between mark and space frequency. Figure 4 shows the binary input to FSK modulator and corresponding FSK output.

37 When the binary input (f b ) changes from a logic 1 to logic 0 and vice versa, the FSK output frequency shifts from a mark frequency (f m ) to a space frequency (f S ) and vice versa. The mark frequency is the higher frequency (f C + f) and the space frequency is the lower frequency (f C - f). The truth table for binary FSK modulator shows the input and output possibilities for a given digital modulation scheme. FSK Bit Rate, Baud and Bandwidth: The time of one bit (t b ) is same as the time the FSK output is a mark or space frequency (t S ). The bit time is equal to the time of FSK signaling element. Therefore, the bit rate is equal to baud. For N=1, Baud = (f b /N) = f b.

38 FSK is exception to the rule for digital modulation as minimum bandwidth is not determined from B = (f b /N). The minimum bandwidth for FSK is, Equation (21) resembles the Carson s rule for determining the approximate bandwidth for an FM wave. The difference is, for FSK, the bit rate (f b ) is substituted for the modulating signal frequency (f m ). Bessel function can also be used to determine approximate bandwidth for FSK wave. Time of one bit, t b = (1/f b ). where f m is the mark frequency.

39 f s is the space frequency. T 1 is the period of shortest cycle. (1/T 1 ) is the fundamental frequency of the binary square wave. f b is the input bit rate in bps. The fastest rate of change (highest fundamental frequency) in a NRZ binary signal occurs when alternating 0 s and 1 s are occurring. (i.e., a square wave). Since it takes a high and a low to produce a cycle, the highest fundamental frequency present in a square wave is equal to the repetition rate of the square wave. For example, with binary signal, it is equal to half the bit rate [i.e.f a = (f b /2)]. where f a is the fundamental frequency of the binary input signal in Hertz. f b is the input bit rate in bps. The formula used for modulation index in FM is valid for FSK. Therefore, h = (unitless) f a where h is the h-factor in FSK, same as modulation index in FM. f a is the fundament The worst case modulation index (deviation ratio) is that which yields widest bandwidth. The worst case/widest bandwidth occurs when both the frequency deviation and modulating signal frequency are at their maximum values. The peak frequency deviation in FSK is constant and always at its maximum value. The highest fundamental frequency is equal to half the incoming bit rate. where h is the h-factor (unitless). f m is the mark frequency in Hertz. f S is the space frequency in Hertz. f b is the bit rate in bps. Problem: 1. Determine the a) peak frequency deviation b) minimum bandwidth and c) baud for a BFSK signal with a mark frequency of 49 KHz, space frequency of 51 KHz and an input bit rate of 2 kbps. 2. Using Bessel Table, determine the minimum bandwidth for the same FSK signal given in problem 1, above.

40 FSK Transmitter: Figure 6 shows a simplified binary FSK modulator. It is very similar to conventional FM modulator and is very often a Voltage Controlled Oscillator (VCO) since the voltage is made constant and only the frequency is varying. The center frequency (f c ) is chosen such that it falls half way between the mark and space frequency. A logic 1 input shifts the VCO output to the mark frequency and a logic 0 input shifts the VCO output to the space frequency. As the binary input changes back and forth between logic 1 and logic 0 conditions, the VCO output also shifts or deviates back and forth between mark and space frequencies. IN BFSK modulator, equal to the difference between the carrier rest frequency and either the mark or space frequency (or half the difference between mark and space frequencies). A VCO FSK modulator can be operated in sweep mode where peak frequency deviation is simply the product of binary input voltage and the deviation sensitivity of VCO. With sweep mode of modulation, frequency deviation is expressed mathematically as 1 V m (t) (24) where peak frequency deviation in Hz. V m (t) is the peak binary modulating signal voltage in volts. K 1 is the deviation sensitivity in Hz/Volt. With BFSK, the amplitude of the input signal can only be one of the two values, one for logic 1 and the other for logic 0 conditions. Therefore the peak frequency deviation is constant and is always at its maximum value. The frequency deviation is simply plus or minus the peak voltage of the binary signal times the deviation sensitivity of the VCO. Since the peak voltage is same for a logic 1 as it is for logic 0, the magnitude of frequency deviation is also the same for logic 1 as it is for logic 0.

41 FSK Receiver: FSK demodulation is quite simple as shown in Figure 7. The FSK input signal is simultaneously applied to the inputs of both band pass filters (BPF) through a power splitter. The respective filter passes only the mark or only the space frequency on to its respective envelope detector. Envelope detectors indicate the total power in each passband and the comparator responds to the largest of the two powers. This type of FSK detection is referred as non-coherent detection since there is no frequency involved in the demodulation process that is synchronized either in phase, frequency or both with the incoming signal.

42 The incoming FSK signal is multiplied by a recovered carrier signal that has the exact same frequency and phase as the transmitter reference. The two transmitted frequencies (mark and space frequencies) are not generally continuous; so it is not practical to produce a local reference that is coherent with both of them. The coherent FSK detection is seldom used. The most common circuit used for demodulating BFSK signal is PLL-FSK detector. It works similar to PLL-FM demodulator. As the input to PLL shifts between the mark and space frequencies, the dc error voltage at the output of phase comparator follows the frequency shift. Since only two input frequencies are used, there are also only two output error voltages. One represents logic 1 and the other represents logic 0. Therefore, the output is a two-level (binary) representation of FSK input. Generally the natural frequency of the PLL is equal to the center frequency of FSK demodulator. The changes in the dc error voltage follow the changes in the analog input frequency and are symmetrical around 0V. Figure.10 Input and Output Waveforms of PLL FSK Demodulator

43 Advantages of FSK: Since FSK is a robust scheme, it is used in telegraphy systems. It is reliable in the presence of noise. It is possible to use more than two frequencies to increase the symbol rate. Disadvantages of FSK: BFSK is not efficient in terms of bandwidth since each symbol has only two possible states. High frequency radio channel tend to be very noisy and phase shifts are introduced into the signal when it is traveled through the ionosphere. So, it is impractical to maintain accurate phase information. It provides only low data rate for high frequency communication. Applications of FSK: FSK is used for low data rate applications such as pagers. It is used for transmitting burst of data over systems that are mainly analog. It is used extensively in high frequency radio systems for radio teletype transmission. It is used in VHF Amateur radio link. Gausian minimum shift keying (GMSK) which is a special case of FSK is used in Global system for mobile communication (GSM) cellular radio and Personal Communication System (PCS). It is also used in telephone transmission system. Continuous Phase FSK: The continuous-phase FSK is a binary FSK where the mark and space frequencies are synchronized with the binary input bit rate. Synchronous implies that there is a precise time relationship between two frequencies; it does not mean both are equal. The mark and space frequencies are selected in such a way that they are separated from the center frequency by an exact multiple of one half the bit rate [f m = f s = n (f b /2) where n is any integer]. It provides a smooth phase transition in analog output signal when it changes from f s to f m and vice versa. It avoids phase discontinuity between f s and f m when the binary input changes from logic 0 to logic 1. Advantage: It provides better error performance than conventional BFSK for a given SNR. Disadvantage: It requires synchronization circuits and is more expensive to implement.

44 Self Study 4: 1. DAM is otherwise called as. 2. The phase shift in carrier frequency ( f) is to the amplitude of the binary input signal v m (t). a) indirectly proportional b) equal to c) directly proportional 3. is a special case of FSK is used in GSM and PCS. a) BFSK b) DAM c) ASK d) GMSK 4. Say True / False a) In FSK, bit rate is not equal to the baud rate. b) In FSK, The highest fundamental frequency is equal to half the incoming bit rate. Self Study 4 Answers: 1. ASK 2. c) 3. d) 4. a) False b) True Phase Shift Keying (PSK): Phase Shift Keying is also another form of angle modulated, constant amplitude digital modulation. It is an M-ary digital modulation scheme similar to conventional Phase Modulation except with PSK, the input is a binary digital signal and limited number of output phases are possible. The input binary information is encoded into groups of bits before modulating the carrier. The number of output phases is defined by M = 2 N and determined by the number of bits (N) in the group.

45 Binary Phase Shift Keying (BPSK): BPSK is the simplest form of Phase shift keying where N = 1 and M = 2 N = 2. With BPSK, two phases are possible for carrier, one phase represents logic 1 and the other phase represents a logic 0. As the input digital signal changes the state from logic 1 to logic 0 or logic 0 to logic 1, the phase of the output carrier shifts between the two angles separated by 180. It is also called as Phase Reversal Keying (PRK) or Biphase modulation. BPSK is a form of square wave modulation of a continuous wave signal. BPSK Transmitter: Figure 11 shows the simplified block diagram of a BPSK Transmitter. Here the balanced modulator acts as a phase reversing switch. Since bipolar signals are more power efficient to encode binary data with voltages equal in magnitude but opposite in polarity and symmetrically balanced about 0V. Assume 1 level of 0V required an average power of 12.5W, assuming equal probability of occurrence for logic 0 and logic 1. With logic 1 of +2.5V and logic 0 of -2.5V, the average power is 6.25W. By using bipolar symmetrical voltages, the average power is reduced by a factor of 50%. So a level converter is needed in BPSK transmitter to get a bipolar signal since more power efficient. The balanced modulators are balanced mixers or balanced diode mixers or product modulators or product detectors. It is used extensively in both

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